Relativity and Quantum Mechanics

From my understanding and from what I have read Quantum Mechanics and Relativity do not mix well. I understand that Quantum mechanics gives you probabilities and relativity gives you a more define answer. Is that the only reason why they don't mix? Are there other reasons?

It's quantum mechanics doesn't mix well with general relativity. Special relativistic quantum mechanics is a perfectly well defined field.

They don't mix well because nobody has as yet been able to coherently combine them. The two theories describe different things. One describes gravity (general relativity), and the other describes the other 3 forces of nature. Roughly speaking, nobody has been able to straightforwardly combine the two in a way that does not give you a bunch of infinities everywhere.

There are some attempts like string theory, and loop quantum gravity, but they are basically wholly new theories, and they all contain parts that have not yet been worked out.

QM and GR work just fine together at low energies. It is entirely incorrect to say that QM and GR cannot be made compatible. They certainly can below certain cutoffs. The issue, if you want to call it that, is what happens at high enough energy scales where new physics is needed because GR is non-perturbative on these scales. We can calculate scattering cross sections in low energy quantum gravity using QFT just as well as we can calculate cross sections in QED. I would highly reccomend reading section 22.4 of Schwartz "Quantum Field Theory and the Standard Model". There you will find a calculation of the 1-loop diagram for the graviton propagator corresponding to vacuum polarization and the result is perturbative, regular, and predictive. In inflationary cosmology we quantize metric perturbations to get gravitational waves generated by a scalar inflaton, just like we quantize the EM field. This is in fact testable by relating the power spectrum of these quantized tensor modes to the energy scale of inflation.